This project is designed to mount a substantial attack on a number of practically important topics in the analysis of time to response or 'failure time' date. The methodological starting point for most of the proposed work is the so-called proportional hazards (ph) regression model in which study subject characteristics or exposure variables are presumed to affect the (instantaneous) failure rate in a multiplicative manner. This model is aminable to generalizations and modifications that allow a number of important failure time topic to be addressed. These topics, listed below, are particularly relevant to the analysis of complex epidemiological or clinical cohort studies in which there is limited ability to control the characteristics or exposure variables under study. The topics are also important for therapeutic trials and laboratory experiments, for example, in animal carcinogenesis. Data analytic topics of emphasis will include (1) theoretical and practical aspects of the use of time-dependent covariates that may record, throughout the observation period, study subject characteristics and exposure levels, (2) the joint analysis of multivariate failure times, as is required when individual study subjects may experience several failure times, (3) the accomodation of multiple failure types or competing risks and, in particular the study of interrelations among failure types and (4) the accomodation of missing covariate data, including circumstances in which the missing data rate depends on the corresponding failure time(s). A number of additional topics will also be considered including the standardization of 'mortality' rates to an external population using the ph model to adjust for demographic characteristics; parameter transformations to improve interval estimation for survival curves; goodness of fit testing for the ph model; efficiency and robustness of ph estimation; and the analysis of very large failure time data sets. Adaptation of methodological developments to case-control study designs and low dose extrapolation studies will also be considered.